The operational matrix of polynomial series transformation
Panagiotis Demetriou Sparis, Spyridon G. Mouroutsos · International Journal of Systems Science · 1985
This paper introduces the operational matrix of polynomial series transformation T that may be applied to transform any polynomial series basis vector to the Taylor polynomials. The matrix is determined for most commonly used polynomial series expansions, such as the Chebyshev, the Laguerre, the Legendre and the Hermite. Using the polynomial series transformation matrix, the corresponding operational matrix of integration of a polynomial series, may easily be determined. Finally, it is shown that all the approximate methods using polynomial-based operational matrices of integration may be connected to the Taylor-series method.